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Article 3098 of comp.ai.philosophy:
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>From: orourke@unix1.cs.umass.edu (Joseph O'Rourke)
Newsgroups: comp.ai.philosophy
Subject: Re: Intelligence Testing
Message-ID: <42196@dime.cs.umass.edu>
Date: 24 Jan 92 04:15:08 GMT
References: <11819@optima.cs.arizona.edu>
Sender: news@dime.cs.umass.edu
Reply-To: orourke@sophia.smith.edu (Joseph O'Rourke)
Organization: Smith College, Northmapton, MA, US
Lines: 25

In article <11819@optima.cs.arizona.edu> gudeman@cs.arizona.edu (David Gudeman) writes:
>In article  <42139@dime.cs.umass.edu> Joseph O'Rourke writes:
>]And I believe this:
>]	[*] If a subject does not fully grasp the meaning of X,
>]	then there are a series of questions about X that will 
>]	reveal this.
>]Every teacher who has composed an exam believes this.  The flip side
>]of [*] is that if a long series of such questions are answered
>]correctly, our confidence that the subject does indeed grasp X
>]increases without bound.
>
>That is a logical fallacy in that you are starting with a sentence of
>the form "(not P) implies Q" and are drawing conclusions based on a
>sentence of the form "(not Q) implies P".  As any freshman in a logic
>class can tell you, you cannot make logical inferences about the
>antecedent from the truth or falsehood of the consequent.

I thought that ~P => Q is logically equivalent to ~Q => P, so that
from ~P => Q and ~Q, P follows.  Or in other words, if I believe
~P => Q is true, and I gain evidence that Q is false, then I should
conclude that ~P is false, so P is true.  This is making 
"logical inferences about the antecedent from the ... falsehood of 
the consequent."  What am I missing here?  Maybe you are saying
I am not justified in believing ~P => Q ([*] above) in the first
place?


